Uncertain Reasoning

1
Uncertain Reasoning

• Dempster-Shafer theory (cont.)

2
Dempster-Shafer theory of evidence

• Knowledge representation issues let O ?1,
  ..., ?n.
• If ?i is known to be the true value, then
• m(?i) 1.
• m(A) 0 otherwise.

3
Dempster-Shafer theory of evidence

• Knowledge representation issues bayesian
  special case.
• If m(?i) is known for every element ?i of O,
  then there is no ignorance and the probabilities
  of all events are known
• Si1nm(?i) 1.
• m(A) 0 if A is not a singleton.

4
Dempster-Shafer theory of evidence

• Knowledge representation issues total
  ignorance.
• The case of total ignorance about the
  probabilities of events can be characterised as
  follows
• m(O) 1.
• m(A) 0 for every A c O such that A ? O.

5
Dempster-Shafer theory of evidence

• Knowledge representation issues information
  fusion.
• One of the most important and interesting
  features of the Dempster-Shafer theory of
  evidence is the ability to combine information
  from different independent sources. For example,
  assume that two sensors inform two different mass
  distributions m1 and m2. Evidently, we assume
  that the domain O is the same for both sensors.

6
Dempster-Shafer theory of evidence

• Knowledge representation issues information
  fusion.
• K S A, B A n B m1(A)m2(B).
• If K lt 1, then information fusion is possible.

7
Dempster-Shafer theory of evidence

• Knowledge representation issues information
  fusion m1 m2.
• If C ? , then(m1 m2)(C) (1/K) S A, B A
  n B C m1(A)m2(B).
• Otherwise, (m1 m2)( ) 0.

8
Dempster-Shafer theory of evidence

• Knowledge representation issues information
  fusion m1 m2.
• (m1 m2)(C) is commutative and associative.